The impact of macroscopic epistasis on long-term evolutionary dynamics

Environment-independent distribution of mutational effects emerges from microscopic epistasis

Predicting how new mutations alter phenotypes is difficult because mutational effects vary across genotypes and environments. Recently discovered global epistasis, where the fitness effects of mutations scale with the fitness of the background genotype, can improve predictions, but how the environment modulates this scaling is unknown. We measured the fitness effects of ~100 insertion mutations in 42 strains of Saccharomyces cerevisiae in six laboratory environments and found that the global-epistasis scaling is nearly invariant across environments. Instead, the environment tunes one global parameter, the background fitness at which most mutations switch sign. As a consequence, the distribution of mutational effects is predictable across genotypes and environments. Our results suggest that the effective dimensionality of genotype-to-phenotype maps across environments is surprisingly low.

Effects of selection stringency on the outcomes of directed evolution

Directed evolution makes mutant lineages compete in climbing complicated sequence-function landscapes. Given this underlying complexity it is unclear how selection stringency, a ubiquitous parameter of directed evolution, impacts the outcome. Here we approach this question in terms of the fitnesses of the candidate variants at each round and the heterogeneity of their distributions of fitness effects. We show that even if the fittest mutant is most likely to yield the fittest mutants in the next round of selection, diversification can improve outcomes by sampling a larger variety of fitness effects. We find that heterogeneity in fitness effects between variants, larger population sizes, and evolution over a greater number of rounds all encourage diversification.

The distribution of beneficial mutational effects between two sister yeast species poorly explains natural outcomes of vineyard adaptation

Domesticated strains of Saccharomyces cerevisiae have adapted to resist copper and sulfite, two chemical stressors commonly used in winemaking. S. paradoxus, has not adapted to these chemicals despite being consistently present in sympatry with S. cerevisiae in vineyards. This contrast represents a case of apparent evolutionary constraints favoring greater adaptive capacity in S. cerevisiae. In this study, we used a comparative mutagenesis approach to test whether S. paradoxus is mutationally constrained with respect to acquiring greater copper and sulfite resistance. For both species, we assayed the rate, effect size, and pleiotropic costs of resistance mutations and sequenced a subset of 150 mutants isolated from our screen. We found that the distributions of mutational effects displayed by the two species were very similar and poorly explained the natural pattern. We also found that chromosome VIII aneuploidy and loss of function mutations in PMA1 confer copper resistance in both species, whereas loss of function mutations in REG1 were only a viable route to copper resistance in S. cerevisiae. We also observed a single de novo duplication of the CUP1 gene in S. paradoxus but none in S. cerevisiae. For sulfite, loss of function mutations in RTS1 and KSP1 confer resistance in both species, but mutations in RTS1 have larger average effects in S. paradoxus. Our results show that even when the distributions of mutational effects are largely similar, species can differ in the adaptive paths available to them. They also demonstrate that assays of the distribution of mutational effects may lack predictive insight concerning adaptive outcomes.

How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution

The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population's mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.

Changing fitness effects of mutations through long-term bacterial evolution

The distribution of fitness effects of new mutations shapes evolution, but it is challenging to observe how it changes as organisms adapt. Using Escherichia coli lineages spanning 50,000 generations of evolution, we quantify the fitness effects of insertion mutations in every gene. Macroscopically, the fraction of deleterious mutations changed little over time whereas the beneficial tail declined sharply, approaching an exponential distribution. Microscopically, changes in individual gene essentiality and deleterious effects often occurred in parallel; altered essentiality is only partly explained by structural variation. The identity and effect sizes of beneficial mutations changed rapidly over time, but many targets of selection remained predictable because of the importance of loss-of-function mutations. Taken together, these results reveal the dynamic-but statistically predictable-nature of mutational fitness effects.

A dynamical limit to evolutionary adaptation

Natural selection makes evolutionary adaptation possible even if the overwhelming majority of new mutations are deleterious. However, in rapidly evolving populations where numerous linked mutations occur and segregate simultaneously, clonal interference and genetic hitchhiking can limit the efficiency of selection, allowing deleterious mutations to accumulate over time. This can in principle overwhelm the fitness increases provided by beneficial mutations, leading to an overall fitness decline. Here, we analyze the conditions under which evolution will tend to drive populations to higher versus lower fitness. Our analysis focuses on quantifying the boundary between these two regimes, as a function of parameters such as population size, mutation rates, and selection pressures. This boundary represents a state in which adaptation is precisely balanced by Muller's ratchet, and we show that it can be characterized by rapid molecular evolution without any net fitness change. Finally, we consider the implications of global fitness-mediated epistasis and find that under some circumstances, this can drive populations toward the boundary state, which can thus represent a long-term evolutionary attractor.

A dynamical limit to evolutionary adaptation

Natural selection makes evolutionary adaptation possible even if the overwhelming majority of new mutations are deleterious. However, in rapidly evolving populations where numerous linked mutations occur and segregate simultaneously, clonal interference and genetic hitchhiking can limit the efficiency of selection, allowing deleterious mutations to accumulate over time. This can in principle overwhelm the fitness increases provided by beneficial mutations, leading to an overall fitness decline. Here, we analyze the conditions under which evolution will tend to drive populations to higher versus lower fitness. Our analysis focuses on quantifying the boundary between these two regimes, as a function of parameters such as population size, mutation rates, and selection pressures. This boundary represents a state in which adaptation is precisely balanced by Muller's ratchet, and we show that it can be characterized by rapid molecular evolution without any net fitness change. Finally, we consider the implications of global fitness-mediated epistasis, and find that under some circumstances this can drive populations towards the boundary state, which can thus represent a long-term evolutionary attractor.

Epistasis and evolution: recent advances and an outlook for prediction

As organisms evolve, the effects of mutations change as a result of epistatic interactions with other mutations accumulated along the line of descent. This can lead to shifts in adaptability or robustness that ultimately shape subsequent evolution. Here, we review recent advances in measuring, modeling, and predicting epistasis along evolutionary trajectories, both in microbial cells and single proteins. We focus on simple patterns of global epistasis that emerge in this data, in which the effects of mutations can be predicted by a small number of variables. The emergence of these patterns offers promise for efforts to model epistasis and predict evolution.

Quantifying the local adaptive landscape of a nascent bacterial community

The fitness effects of all possible mutations available to an organism largely shape the dynamics of evolutionary adaptation. Yet, whether and how this adaptive landscape changes over evolutionary times, especially upon ecological diversification and changes in community composition, remains poorly understood. We sought to fill this gap by analyzing a stable community of two closely related ecotypes ("L" and "S") shortly after they emerged within the E. coli Long-Term Evolution Experiment (LTEE). We engineered genome-wide barcoded transposon libraries to measure the invasion fitness effects of all possible gene knockouts in the coexisting strains as well as their ancestor, for many different, ecologically relevant conditions. We find consistent statistical patterns of fitness effect variation across both genetic background and community composition, despite the idiosyncratic behavior of individual knockouts. Additionally, fitness effects are correlated with evolutionary outcomes for a number of conditions, possibly revealing shifting patterns of adaptation. Together, our results reveal how ecological and epistatic effects combine to shape the adaptive landscape in a nascent ecological community.

Fitness of evolving bacterial populations is contingent on deep and shallow history but only shallow history creates predictable patterns

Long-term evolution experiments have tested the importance of genetic and environmental factors in influencing evolutionary outcomes. Differences in phylogenetic history, recent adaptation to distinct environments and chance events, all influence the fitness of a population. However, the interplay of these factors on a population's evolutionary potential remains relatively unexplored. We tracked the outcome of 2000 generations of evolution of four natural isolates of Escherichia coli bacteria that were engineered to also create differences in shallow history by adding previously identified mutations selected in a separate long-term experiment. Replicate populations started from each progenitor evolved in four environments. We found that deep and shallow phylogenetic histories both contributed significantly to differences in evolved fitness, though by different amounts in different selection environments. With one exception, chance effects were not significant. Whereas the effect of deep history did not follow any detectable pattern, effects of shallow history followed a pattern of diminishing returns whereby fitter ancestors had smaller fitness increases. These results are consistent with adaptive evolution being contingent on the interaction of several evolutionary forces but demonstrate that the nature of these interactions is not fixed and may not be predictable even when the role of chance is small.

Selection in a growing colony biases results of mutation accumulation experiments

Mutations provide the raw material for natural selection to act. Therefore, understanding the variety and relative frequency of different type of mutations is critical to understanding the nature of genetic diversity in a population. Mutation accumulation (MA) experiments have been used in this context to estimate parameters defining mutation rates, distribution of fitness effects (DFE), and spectrum of mutations. MA experiments can be performed with different effective population sizes. In MA experiments with bacteria, a single founder is grown to a size of a colony (~ 10⁸). It is assumed that natural selection plays a minimal role in dictating the dynamics of colony growth. In this work, we simulate colony growth via a mathematical model, and use our model to mimic an MA experiment. We demonstrate that selection ensures that, in an MA experiment, fraction of all mutations that are beneficial is over-represented by a factor of almost two, and that the distribution of fitness effects of beneficial and deleterious mutations are inaccurately captured in an MA experiment. Given this, the estimate of mutation rates from MA experiments is non-trivial. We then perform an MA experiment with 160 lines of E. coli, and show that due to the effect of selection in a growing colony, the size and sector of a colony from which the experiment is propagated impacts the results. Overall, we demonstrate that the results of MA experiments need to be revisited taking into account the action of selection in a growing colony.

Challenges and potential solutions for studying the genetic and phenotypic architecture of adaptation in microbes

All organisms are defined by the makeup of their DNA. Over billions of years, the structure and information contained in that DNA, often referred to as genetic architecture, have been honed by a multitude of evolutionary processes. Mutations that cause genetic elements to change in a way that results in beneficial phenotypic change are more likely to survive and propagate through the population in a process known as adaptation. Recent work reveals that the genetic targets of adaptation are varied and can change with genetic background. Further, seemingly similar adaptive mutations, even within the same gene, can have diverse and unpredictable effects on phenotype. These challenges represent major obstacles in predicting adaptation and evolution. In this review, we cover these concepts in detail and identify three emerging synergistic solutions: higher-throughput evolution experiments combined with updated genotype-phenotype mapping strategies and physiological models. Our review largely focuses on recent literature in yeast, and the field seems to be on the cusp of a new era with regard to studying the predictability of evolution.

Modes of Selection in Tumors as Reflected by Two Mathematical Models and Site Frequency Spectra

The tug-of-war model was developed in a series of papers of McFarland and co-authors to account for existence of mutually counteracting rare advantageous driver mutations and more frequent slightly deleterious passenger mutations in cancer. In its original version, it was a state-dependent branching process. Because of its formulation, the tug-of-war model is of importance for tackling the problem as to whether evolution of cancerous tumors is "Darwinian" or "non-Darwinian." We define two Time-Continuous Markov Chain versions of the model, including identical mutation processes but adopting different drift and selection components. In Model A, drift and selection process preserves expected fitness whereas in Model B it leads to non-decreasing expected fitness. We investigate these properties using mathematical analysis and extensive simulations, which detect the effect of the so-called drift barrier in Model B but not in Model A. These effects are reflected in different structure of clone genealogies in the two models. Our work is related to the past theoretical work in the field of evolutionary genetics, concerning the interplay among mutation, drift and selection, in absence of recombination (asexual reproduction), where epistasis plays a major role. Finally, we use the statistics of mutation frequencies known as the Site Frequency Spectra (SFS), to compare the variant frequencies in DNA of sequenced HER2+ breast cancers, to those based on Model A and B simulations. The tumor-based SFS are better reproduced by Model A, pointing out a possible selection pattern of HER2+ tumor evolution. To put our models in context, we carried out an exploratory study of how publicly accessible data from breast, prostate, skin and ovarian cancers fit a range of models found in the literature.

Mutational robustness changes during long-term adaptation in laboratory budding yeast populations

As an adapting population traverses the fitness landscape, its local neighborhood (i.e., the collection of fitness effects of single-step mutations) can change shape because of interactions with mutations acquired during evolution. These changes to the distribution of fitness effects can affect both the rate of adaptation and the accumulation of deleterious mutations. However, while numerous models of fitness landscapes have been proposed in the literature, empirical data on how this distribution changes during evolution remains limited. In this study, we directly measure how the fitness landscape neighborhood changes during laboratory adaptation. Using a barcode-based mutagenesis system, we measure the fitness effects of 91 specific gene disruption mutations in genetic backgrounds spanning 8000–10,000 generations of evolution in two constant environments. We find that the mean of the distribution of fitness effects decreases in one environment, indicating a reduction in mutational robustness, but does not change in the other. We show that these distribution-level patterns result from differences in the relative frequency of certain patterns of epistasis at the level of individual mutations, including fitness-correlated and idiosyncratic epistasis.

Complex fitness landscape shapes variation in a hyperpolymorphic species

It is natural to assume that patterns of genetic variation in hyperpolymorphic species can reveal large-scale properties of the fitness landscape that are hard to detect by studying species with ordinary levels of genetic variation. Here, we study such patterns in a fungus Schizophyllum commune, the most polymorphic species known. Throughout the genome, short-range linkage disequilibrium (LD) caused by attraction of minor alleles is higher between pairs of nonsynonymous than of synonymous variants. This effect is especially pronounced for pairs of sites that are located within the same gene, especially if a large fraction of the gene is covered by haploblocks, genome segments where the gene pool consists of two highly divergent haplotypes, which is a signature of balancing selection. Haploblocks are usually shorter than 1000 nucleotides, and collectively cover about 10% of the S. commune genome. LD tends to be substantially higher for pairs of nonsynonymous variants encoding amino acids that interact within the protein. There is a substantial correlation between LDs at the same pairs of nonsynonymous mutations in the USA and the Russian populations. These patterns indicate that selection in S. commune involves positive epistasis due to compensatory interactions between nonsynonymous alleles. When less polymorphic species are studied, analogous patterns can be detected only through interspecific comparisons.

Changes to DNA known as mutations may alter how the proteins and other components of a cell work, and thus play an important role in allowing living things to evolve new traits and abilities over many generations. Whether a mutation is beneficial or harmful may differ depending on the genetic background of the individual – that is, depending on other mutations present in other positions within the same gene – due to a phenomenon called epistasis.

Epistasis is known to affect how various species accumulate differences in their DNA compared to each other over time. For example, a mutation that is rare in humans and known to cause disease may be widespread in other primates because its negative effect is canceled out by another mutation that is standard for these species but absent in humans. However, it remains unclear whether epistasis plays a significant part in shaping genetic differences between individuals of the same species.

A type of fungus known as Schizophyllum commune lives on rotting wood and is found across the world. It is one of the most genetically diverse species currently known, so there is a higher chance of pairs of compensatory mutations occurring and persisting for a long time in S. commune than in most other species, providing a unique opportunity to study epistasis.

Here, Stolyarova et al. studied two distinct populations of S. commune, one from the USA and one from Russia. The team found that – unlike in humans, flies and other less genetically diverse species – epistasis maintains combinations of mutations in S. commune that individually would be harmful to the fungus but together compensate for each other. For example, pairs of mutations affecting specific molecules known as amino acids – the building blocks of proteins – that physically interact with each other tended to be found together in the same individuals.

One potential downside of having pairs of compensatory mutations in the genome is that when the organism reproduces, the process of making sex cells may split up these pairs so that harmful mutations are inherited without their partner mutations. Thus, epistasis may have helped shape the way S. commune and other genetically diverse species have evolved.

Seed banks alter the molecular evolutionary dynamics of Bacillus subtilis

Fluctuations in the availability of resources constrain the growth and reproduction of individuals, which subsequently affects the evolution of their respective populations. Many organisms contend with such fluctuations by entering a reversible state of reduced metabolic activity, a phenomenon known as dormancy. This pool of dormant individuals (i.e. a seed bank) does not reproduce and is expected to act as an evolutionary buffer, though it is difficult to observe this effect directly over an extended evolutionary timescale. Through genetic manipulation, we analyze the molecular evolutionary dynamics of Bacillus subtilis populations in the presence and absence of a seed bank over 700 days. The ability of these bacteria to enter a dormant state increased the accumulation of genetic diversity over time and altered the trajectory of mutations, findings that were recapitulated using simulations based on a mathematical model of evolutionary dynamics. While the ability to form a seed bank did not alter the degree of negative selection, we found that it consistently altered the direction of molecular evolution across genes. Together, these results show that the ability to form a seed bank can affect the direction and rate of molecular evolution over an extended evolutionary timescale.

Population genetics of polymorphism and divergence in rapidly evolving populations

In rapidly evolving populations, numerous beneficial and deleterious mutations can arise and segregate within a population at the same time. In this regime, evolutionary dynamics cannot be analyzed using traditional population genetic approaches that assume that sites evolve independently. Instead, the dynamics of many loci must be analyzed simultaneously. Recent work has made progress by first analyzing the fitness variation within a population, and then studying how individual lineages interact with this traveling fitness wave. However, these "traveling wave" models have previously been restricted to extreme cases where selection on individual mutations is either much faster or much slower than the typical coalescent timescale Tc. In this work, we show how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (Tcs) are neither large nor small compared to one. This enables us to describe the dynamics of populations subject to a wide range of fitness effects, and in particular, in cases where it is not immediately clear which mutations are most important in shaping the dynamics and statistics of genetic diversity. We use this approach to derive new expressions for the fixation probabilities and site frequency spectra of mutations as a function of their scaled fitness effects, along with related results for the coalescent timescale Tc and the rate of adaptation or Muller's ratchet. We find that competition between linked mutations can have a dramatic impact on the proportions of neutral and selected polymorphisms, which is not simply summarized by the scaled selection coefficient Tcs. We conclude by discussing the implications of these results for population genetic inferences.

The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and while it is known to slow down the rate of adaptation (when compared to the strong-selection, weak-mutation model with the same parameters), how it affects the shape of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the shape of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the rescaled fitness trajectory (where adaptation speed is measured relative to its value at the start of the experiment), while an enhancement of the beneficial mutation rate does the opposite of slowing it down. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs change in fraction of beneficial mutations).

The population genetics of collateral resistance and sensitivity

Resistance mutations against one drug can elicit collateral sensitivity against other drugs. Multi-drug treatments exploiting such trade-offs can help slow down the evolution of resistance. However, if mutations with diverse collateral effects are available, a treated population may evolve either collateral sensitivity or collateral resistance. How to design treatments robust to such uncertainty is unclear. We show that many resistance mutations in Escherichia coli against various antibiotics indeed have diverse collateral effects. We propose to characterize such diversity with a joint distribution of fitness effects (JDFE) and develop a theory for describing and predicting collateral evolution based on simple statistics of the JDFE. We show how to robustly rank drug pairs to minimize the risk of collateral resistance and how to estimate JDFEs. In addition to practical applications, these results have implications for our understanding of evolution in variable environments.

Drugs known as antibiotics are the main treatment for most serious infections caused by bacteria. However, many bacteria are acquiring genetic mutations that make them resistant to the effects of one or more types of antibiotics, making them harder to eliminate.

One way to tackle drug-resistant bacteria is to develop new types of antibiotics; however, in recent years, the rate at which new antibiotics have become available has been dwindling. Using two or more existing drugs, one after another, can also be an effective way to eliminate resistant bacteria. The success of any such ‘multi-drug’ treatment lies in being able to predict whether mutations that make the bacteria resistant to one drug simultaneously make it sensitive to another, a phenomenon known as collateral sensitivity.

Different resistance mutations may have different collateral effects: some may increase the bacteria’s sensitivity to the second drug, while others might make the bacteria more resistant. However, it is currently unclear how to design robust multi-drug treatments that take this diversity of collateral effects into account.

Here, Ardell and Kryazhimskiy used a concept called JDFE (short for the joint distribution of fitness effects) to describe the diversity of collateral effects in a population of bacteria exposed to a single drug. This information was then used to mathematically model how collateral effects evolved in the population over time.

Ardell and Kryazhimskiy showed that this approach can predict how likely a population is to become collaterally sensitive or collaterally resistant to a second antibiotic. Drug pairs can then be ranked according to the risk of collateral resistance emerging, so long as information on the variety of resistance mutations available to the bacteria are included in the model.

Each year, more than 700,000 people die from infections caused by bacteria that are resistant to one or more antibiotics. The findings of Ardell and Kryazhimskiy may eventually help clinicians design multi-drug treatments that effectively eliminate bacterial infections and help to prevent more bacteria from evolving resistance to antibiotics. However, to achieve this goal, more research is needed to fully understand the range collateral effects caused by resistance mutations.

Extreme value theory as a framework for understanding mutation frequency distribution in cancer genomes

Currently, the population dynamics of preclonal cancer cells before clonal expansion of tumors has not been sufficiently addressed thus far. By focusing on preclonal cancer cell population as a Darwinian evolutionary system, we formulated and analyzed the observed mutation frequency among tumors (MFaT) as a proxy for the hypothesized sequence read frequency and beneficial fitness effect of a cancer driver mutation. Analogous to intestinal crypts, we assumed that sample donor patients are separate culture tanks where proliferating cells follow certain population dynamics described by extreme value theory (EVT). To validate this, we analyzed three large-scale cancer genome datasets, each harboring > 10000 tumor samples and in total involving > 177898 observed mutation sites. We clarified the necessary premises for the application of EVT in the strong selection and weak mutation (SSWM) regime in relation to cancer genome sequences at scale. We also confirmed that the stochastic distribution of MFaT is likely of the Fréchet type, which challenges the well-known Gumbel hypothesis of beneficial fitness effects. Based on statistical data analysis, we demonstrated the potential of EVT as a population genetics framework to understand and explain the stochastic behavior of driver-mutation frequency in cancer genomes as well as its applicability in real cancer genome sequence data.

Intra-Population Competition during Adaptation to Increased Temperature in an RNA Bacteriophage

Evolution of RNA bacteriophages of the family Leviviridae is governed by the high error rates of their RNA-dependent RNA polymerases. This fact, together with their large population sizes, leads to the generation of highly heterogeneous populations that adapt rapidly to most changes in the environment. Throughout adaptation, the different mutants that make up a viral population compete with each other in a non-trivial process in which their selective values change over time due to the generation of new mutations. In this work we have characterised the intra-population dynamics of a well-studied levivirus, Qβ, when it is propagated at a higher-than-optimal temperature. Our results show that adapting populations experienced rapid changes that involved the ascent of particular genotypes and the loss of some beneficial mutations of early generation. Artificially reconstructed populations, containing a fraction of the diversity present in actual populations, fixed mutations more rapidly, illustrating how population bottlenecks may guide the adaptive pathways. The conclusion is that, when the availability of beneficial mutations under a particular selective condition is elevated, the final outcome of adaptation depends more on the occasional occurrence of population bottlenecks and how mutations combine in genomes than on the selective value of particular mutations.

The evolutionary origin of the universal distribution of mutation fitness effect

An intriguing fact long defying explanation is the observation of a universal exponential distribution of beneficial mutations in fitness effect for different microorganisms. To explain this effect, we use a population model including mutation, directional selection, linkage, and genetic drift. The multiple-mutation regime of adaptation at large population sizes (traveling wave regime) is considered. We demonstrate analytically and by simulation that, regardless of the inherent distribution of mutation fitness effect across genomic sites, an exponential distribution of fitness effects emerges in the long term. This result follows from the exponential statistics of the frequency of the less-fit alleles, f, that we predict to evolve, in the long term, for both polymorphic and monomorphic sites. We map the logarithmic slope of the distribution onto the previously derived fixation probability and demonstrate that it increases linearly in time. Our results demonstrate a striking difference between the distribution of fitness effects observed experimentally for naturally occurring mutations, and the "inherent" distribution obtained in a directed-mutagenesis experiment, which can have any shape depending on the organism. Based on these results, we develop a new method to measure the fitness effect of mutations for each variable residue using DNA sequences sampled from adapting populations. This new method is not sensitive to linkage effects and does not require the one-site model assumptions.

An Evolutionary Model of Progression to AIDS

The time to the onset of AIDS symptoms in an HIV infected individual is known to correlate inversely with viremia and the level of immune activation. The correlation exists against the background of strong individual fluctuations demonstrating the existence of hidden variables depending on patient and virus parameters. At the moment, prognosis of the time to AIDS based on patient parameters is not possible. In addition, it is of paramount importance to understand the reason of progression to AIDS in untreated patients to be able to learn to control it by means other than anti-retroviral therapy. Here we develop a mechanistic mathematical model to predict the speed of progression to AIDS in individual untreated patients and patients treated with suboptimal therapy, based on a single-time measurement of several virological and immunological parameters. We show that the gradual increase in virus fitness during a chronic infection causes slow gradual depletion of CD4 T cells. Using the existing evolution models of HIV, we obtain general expressions predicting the time to the onset of AIDS symptoms in terms of the patient parameters, for low-viremia and high-viremia patients separately. We show that the evolution model of AIDS fits the existing data on virus-time correlations better than the alternative model of the deregulation of homeostatic response.

Mutation bias can shape adaptation in large asexual populations experiencing clonal interference

The extended evolutionary synthesis invokes a role for development in shaping adaptive evolution, which in population genetics terms corresponds to mutation-biased adaptation. Critics have claimed that clonal interference makes mutation-biased adaptation rare. We consider the behaviour of two simultaneously adapting traits, one with larger mutation rate U, the other with larger selection coefficient s, using asexual travelling wave models. We find that adaptation is dominated by whichever trait has the faster rate of adaptation v in isolation, with the other trait subject to evolutionary stalling. Reviewing empirical claims for mutation-biased adaptation, we find that not all occur in the 'origin-fixation' regime of population genetics where v is only twice as sensitive to s as to U. In some cases, differences in U are at least ten to twelve times larger than differences in s, as needed to cause mutation-biased adaptation even in the 'multiple mutations' regime. Surprisingly, when U > s in the 'diffusive-mutation' regime, the required sensitivity ratio is also only two, despite pervasive clonal interference. Given two traits with identical v, the benefit of having higher s is surprisingly small, occurring largely when one trait is at the boundary between the origin-fixation and multiple mutations regimes.

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

The dynamics of evolution is intimately shaped by epistasis - interactions between genetic elements which cause the fitness-effect of combinations of mutations to be non-additive. Analyzing evolutionary dynamics that involves large numbers of epistatic mutations is intrinsically difficult. A crucial feature is that the fitness landscape in the vicinity of the current genome depends on the evolutionary history. A key step is thus developing models that enable study of the effects of past evolution on future evolution. In this work, we introduce a broad class of high-dimensional random fitness landscapes for which the correlations between fitnesses of genomes are a general function of genetic distance. Their Gaussian character allows for tractable computational as well as analytic understanding. We study the properties of these landscapes focusing on the simplest evolutionary process: random adaptive (uphill) walks. Conventional measures of "ruggedness" are shown to not much affect such adaptive walks. Instead, the long-distance statistics of epistasis cause all properties to be highly conditional on past evolution, determining the statistics of the local landscape (the distribution of fitness-effects of available mutations and combinations of these), as well as the global geometry of evolutionary trajectories. In order to further explore the effects of conditioning on past evolution, we model the effects of slowly changing environments. At long times, such fitness "seascapes" cause a statistical steady state with highly intermittent evolutionary dynamics: populations undergo bursts of rapid adaptation, interspersed with periods in which adaptive mutations are rare and the population waits for more new directions to be opened up by changes in the environment. Finally, we discuss prospects for studying more complex evolutionary dynamics and on broader classes of high-dimensional landscapes and seascapes.

The causes of evolvability and their evolution

Evolvability is the ability of a biological system to produce phenotypic variation that is both heritable and adaptive. It has long been the subject of anecdotal observations and theoretical work. In recent years, however, the molecular causes of evolvability have been an increasing focus of experimental work. Here, we review recent experimental progress in areas as different as the evolution of drug resistance in cancer cells and the rewiring of transcriptional regulation circuits in vertebrates. This research reveals the importance of three major themes: multiple genetic and non-genetic mechanisms to generate phenotypic diversity, robustness in genetic systems, and adaptive landscape topography. We also discuss the mounting evidence that evolvability can evolve and the question of whether it evolves adaptively.

Patterns and Mechanisms of Diminishing Returns from Beneficial Mutations

Diminishing returns epistasis causes the benefit of the same advantageous mutation smaller in fitter genotypes and is frequently observed in experimental evolution. However, its occurrence in other contexts, environment dependence, and mechanistic basis are unclear. Here, we address these questions using 1,005 sequenced segregants generated from a yeast cross. Under each of 47 examined environments, 66-92% of tested polymorphisms exhibit diminishing returns epistasis. Surprisingly, improving environment quality also reduces the benefits of advantageous mutations even when fitness is controlled for, indicating the necessity to revise the global epistasis hypothesis. We propose that diminishing returns originates from the modular organization of life where the contribution of each functional module to fitness is determined jointly by the genotype and environment and has an upper limit, and demonstrate that our model predictions match empirical observations. These findings broaden the concept of diminishing returns epistasis, reveal its generality and potential cause, and have important evolutionary implications.

Stochastic tunneling across fitness valleys can give rise to a logarithmic long-term fitness trajectory

Adaptation, where a population evolves increasing fitness in a fixed environment, is typically thought of as a hill-climbing process on a fitness landscape. With a finite genome, such a process eventually leads the population to a fitness peak, at which point fitness can no longer increase through individual beneficial mutations. Instead, the ruggedness of typical landscapes due to epistasis between genes or DNA sites suggests that the accumulation of multiple mutations (via a process known as stochastic tunneling) can allow a population to continue increasing in fitness. However, it is not clear how such a phenomenon would affect long-term fitness evolution. By using a spin-glass type model for the fitness function that takes into account microscopic epistasis, we find that hopping between metastable states can mechanistically and robustly give rise to a slow, logarithmic average fitness trajectory.

Epistasis detectably alters correlations between genomic sites in a narrow parameter window

Different genomic sites evolve inter-dependently due to the combined action of epistasis, defined as a non-multiplicative contribution of alleles at different loci to genome fitness, and the physical linkage of different loci in genome. Both epistasis and linkage, partially compensated by recombination, cause correlations between allele frequencies at the loci (linkage disequilibrium, LD). The interaction and competition between epistasis and linkage are not fully understood, nor is their relative sensitivity to recombination. Modeling an adapting population in the presence of random mutation, natural selection, pairwise epistasis, and random genetic drift, we compare the contributions of epistasis and linkage. For this end, we use a panel of haplotype-based measures of LD and their various combinations calculated for epistatic and non-epistatic pairs separately. We compute the optimal percentages of detected and false positive pairs in a one-time sample of a population of moderate size. We demonstrate that true interacting pairs can be told apart in a sufficiently short genome within a narrow window of time and parameters. Outside of this parameter region, unless the population is extremely large, shared ancestry of individual sequences generates pervasive stochastic LD for non-interacting pairs masking true epistatic associations. In the presence of sufficiently strong recombination, linkage effects decrease faster than those of epistasis, and the detection of epistasis improves. We demonstrate that the epistasis component of locus association can be isolated, at a single time point, by averaging haplotype frequencies over multiple independent populations. These results demonstrate the existence of fundamental restrictions on the protocols for detecting true interactions in DNA sequence sets.

Epistasis in a Fitness Landscape Defined by Antibody-Antigen Binding Free Energy

Epistasis is the phenomenon by which the effect of a mutation depends on its genetic background. While it is usually defined in terms of organismal fitness, for single proteins, it must reflect physical interactions among residues. Here, we systematically extract the specific contribution pairwise epistasis makes to the physical affinity of antibody-antigen binding relevant to affinity maturation, a process of accelerated Darwinian evolution. We find that, among competing definitions of affinity, the binding free energy is the most appropriate to describe epistasis. We show that epistasis is pervasive, accounting for 25%-35% of variability, of which a large fraction is beneficial. This work suggests that epistasis both constrains, through negative epistasis, and enlarges, through positive epistasis, the set of possible evolutionary paths that can produce high-affinity sequences during repeated rounds of mutation and selection.

Adaptation limits ecological diversification and promotes ecological tinkering during the competition for substitutable resources

Microbial communities can evade competitive exclusion by diversifying into distinct ecological niches. This spontaneous diversification often occurs amid a backdrop of directional selection on other microbial traits, where competitive exclusion would normally apply. Yet despite their empirical relevance, little is known about how diversification and directional selection combine to determine the ecological and evolutionary dynamics within a community. To address this gap, we introduce a simple, empirically motivated model of eco-evolutionary feedback based on the competition for substitutable resources. Individuals acquire heritable mutations that alter resource uptake rates, either by shifting metabolic effort between resources or by increasing the overall growth rate. While these constitutively beneficial mutations are trivially favored to invade, we show that the accumulated fitness differences can dramatically influence the ecological structure and evolutionary dynamics that emerge within the community. Competition between ecological diversification and ongoing fitness evolution leads to a state of diversification-selection balance, in which the number of extant ecotypes can be pinned below the maximum capacity of the ecosystem, while the ecotype frequencies and genealogies are constantly in flux. Interestingly, we find that fitness differences generate emergent selection pressures to shift metabolic effort toward resources with lower effective competition, even in saturated ecosystems. We argue that similar dynamical features should emerge in a wide range of models with a mixture of directional and diversifying selection.

Effective models and the search for quantitative principles in microbial evolution

Microbes evolve rapidly. Yet they do so in idiosyncratic ways, which depend on the specific mutations that are beneficial or deleterious in a given situation. At the same time, some population-level patterns of adaptation are strikingly similar across different microbial systems, suggesting that there may also be simple, quantitative principles that unite these diverse scenarios. We review the search for simple principles in microbial evolution, ranging from the biophysical level to emergent evolutionary dynamics. A key theme has been the use of effective models, which coarse-grain over molecular and cellular details to obtain a simpler description in terms of a few effective parameters. Collectively, these theoretical approaches provide a set of quantitative principles that facilitate understanding, prediction, and potentially control of evolutionary phenomena, though formidable challenges remain due to the ecological complexity of natural populations.

Power law fitness landscapes and their ability to predict fitness

Whether or not evolution by natural selection is predictable depends on the existence of general patterns shaping the way mutations interact with the genetic background. This interaction, also known as epistasis, has been observed during adaptation (macroscopic epistasis) and in individual mutations (microscopic epistasis). Interestingly, a consistent negative correlation between the fitness effect of beneficial mutations and background fitness (known as diminishing returns epistasis) has been observed across different species and conditions. We tested whether the adaptation pattern of an additional species, Schizosaccharomyces pombe, followed the same trend. We used strains that differed by the presence of large karyotype differences and observed the same pattern of fitness convergence. Using these data along with published datasets, we measured the ability of different models to describe adaptation rates. We found that a phenotype-fitness landscape shaped like a power law is able to correctly predict adaptation dynamics in a variety of species and conditions. Furthermore we show that this model can provide a link between the observed macroscopic and microscopic epistasis. It may be very useful in the development of algorithms able to predict the adaptation of microorganisms from measures of the current phenotypes. Overall, our results suggest that even though adaptation quickly slows down, populations adapting to lab conditions may be quite far from a fitness peak.

Recombination Alters the Dynamics of Adaptation on Standing Variation in Laboratory Yeast Populations

The rates and selective effects of beneficial mutations, together with population genetic factors such as population size and recombination rate, determine the outcomes of adaptation and the signatures this process leaves in patterns of genetic diversity. Previous experimental studies of microbial evolution have focused primarily on initially clonal populations, finding that adaptation is characterized by new strongly selected beneficial mutations that sweep rapidly to fixation. Here, we study evolution in diverse outcrossed yeast populations, tracking the rate and genetic basis of adaptation over time. We combine time-serial measurements of fitness and allele frequency changes in 18 populations of budding yeast evolved at different outcrossing rates to infer the drivers of adaptation on standing genetic variation. In contrast to initially clonal populations, we find that adaptation is driven by a large number of weakly selected, linked variants. Populations undergoing different rates of outcrossing make use of this selected variation differently: whereas asexual populations evolve via rapid, inefficient, and highly variable fixation of clones, sexual populations adapt continuously by gradually breaking down linkage disequilibrium between selected variants. Our results demonstrate how recombination can sustain adaptation over long timescales by inducing a transition from selection on genotypes to selection on individual alleles, and show how pervasive linked selection can affect evolutionary dynamics.

Beneficial mutation-selection dynamics in finite asexual populations: a free boundary approach

Using a free boundary approach based on an analogy with ice melting models, we propose a deterministic PDE framework to describe the dynamics of fitness distributions in the presence of beneficial mutations with non-epistatic effects on fitness. Contrarily to most approaches based on deterministic models, our framework does not rely on an infinite population size assumption, and successfully captures the transient as well as the long time dynamics of fitness distributions. In particular, consistently with stochastic individual-based approaches or stochastic PDE approaches, it leads to a constant asymptotic rate of adaptation at large times, that most deterministic approaches failed to describe. We derive analytic formulas for the asymptotic rate of adaptation and the full asymptotic distribution of fitness. These formulas depend explicitly on the population size, and are shown to be accurate for a wide range of population sizes and mutation rates, compared to individual-based simulations. Although we were not able to derive an analytic description for the transient dynamics, numerical computations lead to accurate predictions and are computationally efficient compared to stochastic simulations. These computations show that the fitness distribution converges towards a travelling wave with constant speed, and whose profile can be computed analytically.

Genetic variation in adaptability and pleiotropy in budding yeast

Evolution can favor organisms that are more adaptable, provided that genetic variation in adaptability exists. Here, we quantify this variation among 230 offspring of a cross between diverged yeast strains. We measure the adaptability of each offspring genotype, defined as its average rate of adaptation in a specific environmental condition, and analyze the heritability, predictability, and genetic basis of this trait. We find that initial genotype strongly affects adaptability and can alter the genetic basis of future evolution. Initial genotype also affects the pleiotropic consequences of adaptation for fitness in a different environment. This genetic variation in adaptability and pleiotropy is largely determined by initial fitness, according to a rule of declining adaptability with increasing initial fitness, but several individual QTLs also have a significant idiosyncratic role. Our results demonstrate that both adaptability and pleiotropy are complex traits, with extensive heritable differences arising from naturally occurring variation.

Predicting patterns of long-term adaptation and extinction with population genetics

Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But extinction can result from failure to adapt not only to catastrophes, but also to a backlog of environmental challenges. We model long-term adaptation to long series of small challenges, where fitter populations reach higher population sizes. The population's long-term fitness dynamic is well approximated by a simple stochastic Markov chain model. Long-term persistence occurs when the rate of adaptation exceeds the rate of environmental deterioration for some genotypes. Long-term persistence times are consistent with typical fossil species persistence times of several million years. Immediately preceding extinction, fitness declines rapidly, appearing as though a catastrophe disrupted a stably established population, even though gradual evolutionary processes are responsible. New populations go through an establishment phase where, despite being demographically viable, their extinction risk is elevated. Should the population survive long enough, extinction risk later becomes constant over time.

The Nonstationary Dynamics of Fitness Distributions: Asexual Model with Epistasis and Standing Variation

Various models describe asexual evolution by mutation, selection, and drift. Some focus directly on fitness, typically modeling drift but ignoring or simplifying both epistasis and the distribution of mutation effects (traveling wave models). Others follow the dynamics of quantitative traits determining fitness (Fisher's geometric model), imposing a complex but fixed form of mutation effects and epistasis, and often ignoring drift. In all cases, predictions are typically obtained in high or low mutation rate limits and for long-term stationary regimes, thus losing information on transient behaviors and the effect of initial conditions. Here, we connect fitness-based and trait-based models into a single framework, and seek explicit solutions even away from stationarity. The expected fitness distribution is followed over time via its cumulant generating function, using a deterministic approximation that neglects drift. In several cases, explicit trajectories for the full fitness distribution are obtained for arbitrary mutation rates and standing variance. For nonepistatic mutations, especially with beneficial mutations, this approximation fails over the long term but captures the early dynamics, thus complementing stationary stochastic predictions. The approximation also handles several diminishing returns epistasis models (e.g., with an optimal genotype); it can be applied at and away from equilibrium. General results arise at equilibrium, where fitness distributions display a "phase transition" with mutation rate. Beyond this phase transition, in Fisher's geometric model, the full trajectory of fitness and trait distributions takes a simple form; robust to the details of the mutant phenotype distribution. Analytical arguments are explored regarding why and when the deterministic approximation applies.

Evolution of Mutation Rates in Rapidly Adapting Asexual Populations

Mutator and antimutator alleles often arise and spread in both natural microbial populations and laboratory evolution experiments. The evolutionary dynamics of these mutation rate modifiers are determined by indirect selection on linked beneficial and deleterious mutations. These indirect selection pressures have been the focus of much earlier theoretical and empirical work, but we still have a limited analytical understanding of how the interplay between hitchhiking and deleterious load influences the fates of modifier alleles. Our understanding is particularly limited when clonal interference is common, which is the regime of primary interest in laboratory microbial evolution experiments. Here, we calculate the fixation probability of a mutator or antimutator allele in a rapidly adapting asexual population, and we show how this quantity depends on the population size, the beneficial and deleterious mutation rates, and the strength of a typical driver mutation. In the absence of deleterious mutations, we find that clonal interference enhances the fixation probability of mutators, even as they provide a diminishing benefit to the overall rate of adaptation. When deleterious mutations are included, natural selection pushes the population toward a stable mutation rate that can be suboptimal for the adaptation of the population as a whole. The approach to this stable mutation rate is not necessarily monotonic: even in the absence of epistasis, selection can favor mutator and antimutator alleles that "overshoot" the stable mutation rate by substantial amounts.

Can the experimental evolution programme help us elucidate the genetic basis of adaptation in nature?

There have been a variety of approaches taken to try to characterize and identify the genetic basis of adaptation in nature, spanning theoretical models, experimental evolution studies and direct tests of natural populations. Theoretical models can provide formalized and detailed hypotheses regarding evolutionary processes and patterns, from which experimental evolution studies can then provide important proofs of concepts and characterize what is biologically reasonable. Genetic and genomic data from natural populations then allow for the identification of the particular factors that have and continue to play an important role in shaping adaptive evolution in the natural world. Further to this, experimental evolution studies allow for tests of theories that may be difficult or impossible to test in natural populations for logistical and methodological reasons and can even generate new insights, suggesting further refinement of existing theories. However, as experimental evolution studies often take place in a very particular set of controlled conditions--that is simple environments, a small range of usually asexual species, relatively short timescales--the question remains as to how applicable these experimental results are to natural populations. In this review, we discuss important insights coming from experimental evolution, focusing on four key topics tied to the evolutionary genetics of adaptation, and within those topics, we discuss the extent to which the experimental work compliments and informs natural population studies. We finish by making suggestions for future work in particular a need for natural population genomic time series data, as well as the necessity for studies that combine both experimental evolution and natural population approaches.

Genomic investigations of evolutionary dynamics and epistasis in microbial evolution experiments

Microbial evolution experiments enable us to watch adaptation in real time, and to quantify the repeatability and predictability of evolution by comparing identical replicate populations. Further, we can resurrect ancestral types to examine changes over evolutionary time. Until recently, experimental evolution has been limited to measuring phenotypic changes, or to tracking a few genetic markers over time. However, recent advances in sequencing technology now make it possible to extensively sequence clones or whole-population samples from microbial evolution experiments. Here, we review recent work exploiting these techniques to understand the genomic basis of evolutionary change in experimental systems. We first focus on studies that analyze the dynamics of genome evolution in microbial systems. We then survey work that uses observations of sequence evolution to infer aspects of the underlying fitness landscape, concentrating on the epistatic interactions between mutations and the constraints these interactions impose on adaptation.

Elucidating the molecular architecture of adaptation via evolve and resequence experiments

Evolve and resequence (E&R) experiments use experimental evolution to adapt populations to a novel environment, then next-generation sequencing to analyse genetic changes. They enable molecular evolution to be monitored in real time on a genome-wide scale. Here, we review the field of E&R experiments across diverse systems, ranging from simple non-living RNA to bacteria, yeast and the complex multicellular organism Drosophila melanogaster. We explore how different evolutionary outcomes in these systems are largely consistent with common population genetics principles. Differences in outcomes across systems are largely explained by different starting population sizes, levels of pre-existing genetic variation, recombination rates and adaptive landscapes. We highlight emerging themes and inconsistencies that future experiments must address.

Detecting epistasis from an ensemble of adapting populations

The role that epistasis plays during adaptation remains an outstanding problem, which has received considerable attention in recent years. Most of the recent empirical studies are based on ensembles of replicate populations that adapt in a fixed, laboratory controlled condition. Researchers often seek to infer the presence and form of epistasis in the fitness landscape from the time evolution of various statistics averaged across the ensemble of populations. Here, we provide a rigorous analysis of what quantities, drawn from time series of such ensembles, can be used to infer epistasis for populations evolving under weak mutation on finite-site fitness landscapes. First, we analyze the mean fitness trajectory-that is, the time course of the ensemble average fitness. We show that for any epistatic fitness landscape and starting genotype, there always exists a non-epistatic fitness landscape that produces the exact same mean fitness trajectory. Thus, the presence of epistasis is not identifiable from the mean fitness trajectory. By contrast, we show that two other ensemble statistics-the time evolution of the fitness variance across populations, and the time evolution of the mean number of substitutions-can detect certain forms of epistasis in the underlying fitness landscape.

The rule of declining adaptability in microbial evolution experiments

One of the most recurrent observations after two decades of microbial evolution experiments regards the dynamics of fitness change. In a given environment, low-fitness genotypes are recurrently observed to adapt faster than their more fit counterparts. Since adaptation is the main macroscopic outcome of Darwinian evolution, studying its patterns of change could potentially provide insight into key issues of evolutionary theory, from fixation dynamics to the genetic architecture of organisms. Here, we re-analyze several published datasets from experimental evolution with microbes and show that, despite large differences in the origin of the data, a pattern of inverse dependence of adaptability with fitness clearly emerges. In quantitative terms, it is remarkable to observe little if any degree of idiosyncrasy across systems as diverse as virus, bacteria and yeast. The universality of this phenomenon suggests that its emergence might be understood from general principles, giving rise to the exciting prospect that evolution might be statistically predictable at the macroscopic level. We discuss these possibilities in the light of the various theories of adaptation that have been proposed and delineate future directions of research.